Is there a hotel we can stay at for an early flight that also offers transfer and we can leave our car

Yes a lot if them near the airport do and if not there is always Uber,Lift or taxis. I stayed a hotel three years ago for a weekend trip with am early flight and they let me keep my car parked at the hotel. Took the shuttle to my flight and when I came back took their shuttle to the hotel. I am not sure if it was a Hilton or not.

Yes

Yes, a couple of them.